Math Books for the Persnikkity

I am lucky enough to work with a math-enthusiastic bunch of folks. We often
talk about great papers and books for the student of Math. Here’s my list of my
favorite books from my graduate school days.

So often subjects blend that I am not going to do the usual
Algebra/Analysis/Topology/etc. breakdown. Is Linear Algebra algebra or
analysis? How can you tell in functional analysis or harmonic analysis? I
can’t so I won’t even try! Instead I am grouping them “thematically” e.g. the
way I see them fitting well together! I am only listing the exceptional books
here as there are lots of books we know as classics and the list will be
identical to all of those - Baby Rudin! Lang or Hungerford’s Algebra! Alfor’s
Complex Analysis!

Moreover, I am linking to publisher sites rather than big vendors. You are
fully capable of finding sellers.

Linear Algebra Done Right by Sheldon Axler. This
book basically punts on determinants and instead talks about the properties of
operators!

Fourier Analysis -
An Introduction by Elias M. Stein & Rami Shakarachi. For focussed
and gentle discussion of Fourier Analysis I have never found a clearer
explanation than this book.

Measure and Integration Theory
by Heinz Bauer. Measure theory is pretty dry but so critical. Bauer’s
exposition is concise, to the point, and builds the theory from foundations in
such a way as to never leave difficult gaps.

Beginning Functional Analysis
by Karen Saxe. So many Functional Analysis books are built in exactly the
same way around linear algebra and functionals and duals but Saxe gets you
there with extreme grace.

Ideals, Varieties, and Algorithms -
An Introduction to Computational Algebraic Geometry and Commutative Algebra
by David Cox, John Little, and Donal O’Shea. I am not an algebraist by any
stretch of the imagination but this book is such a nice introduction to
commutative algebra that everyone should read and play with it at least once.

Weighing the Odds -
A course in Probability and Statistics by David Williams. A course in
probability that does not simply jump into Expectation and Distributions but
instead wants to lend intuition to the process.

A Course in Machine Learning by Hal Daume III. This
book, while incomplete, and I have not finished working through it, provides a
great, intuitive, introduction to Machine Learning without a need for a strong
probability background. Intuitive descriptions and gentle prose make for a
fun read.

Have something to contribute? Open an
Issue on
Github and let's have a chat!